No Access Submitted: 19 January 2013 Accepted: 11 March 2013 Published Online: 02 April 2013
J. Math. Phys. 54, 042201 (2013);
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  • Nilanjana Datta
  • Min-Hsiu Hsieh
  • Mark M. Wilde
  • Andreas Winter
We establish a theory of quantum-to-classical rate distortion coding. In this setting, a sender Alice has many copies of a quantum information source. Her goal is to transmit a classical description of the source, obtained by performing a measurement on it, to a receiver Bob, up to some specified level of distortion. We derive a single-letter formula for the minimum rate of classical communication needed for this task. We also evaluate this rate in the case in which Bob has some quantum side information about the source. Our results imply that, in general, Alice's best strategy is a non-classical one, in which she performs a collective measurement on successive outputs of the source.
We acknowledge useful discussions Patrick Hayden. M.M.W. acknowledges support from the Centre de Recherches Mathématiques at the University of Montreal. M.-H.H. received support from the Chancellor's postdoctoral research fellowship, University of Technology Sydney (UTS) and was also partly supported by the National Natural Science Foundation of China (Grant No. 61179030) and the Australian Research Council (Grant No. DP120103776). AW was supported by the Royal Society, the Philip Leverhulme Trust, EC integrated project QAP (contract IST-2005-15848), the STREPs QICS and QCS, and the ERC Advanced Grant “IRQUAT”.
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